Properties

Label 950.2.u.g.99.1
Level $950$
Weight $2$
Character 950.99
Analytic conductor $7.586$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.u (of order \(18\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 99.1
Character \(\chi\) \(=\) 950.99
Dual form 950.2.u.g.499.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.342020 + 0.939693i) q^{2} +(-3.16698 + 0.558424i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.558424 - 3.16698i) q^{6} +(0.0202608 + 0.0116976i) q^{7} +(0.866025 - 0.500000i) q^{8} +(6.89886 - 2.51098i) q^{9} +O(q^{10})\) \(q+(-0.342020 + 0.939693i) q^{2} +(-3.16698 + 0.558424i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.558424 - 3.16698i) q^{6} +(0.0202608 + 0.0116976i) q^{7} +(0.866025 - 0.500000i) q^{8} +(6.89886 - 2.51098i) q^{9} +(-1.08041 - 1.87132i) q^{11} +(2.78500 + 1.60792i) q^{12} +(1.56613 + 0.276152i) q^{13} +(-0.0179217 + 0.0150381i) q^{14} +(0.173648 + 0.984808i) q^{16} +(-2.72922 + 7.49847i) q^{17} +7.34161i q^{18} +(-1.06458 + 4.22690i) q^{19} +(-0.0706976 - 0.0257318i) q^{21} +(2.12799 - 0.375222i) q^{22} +(2.88011 - 3.43239i) q^{23} +(-2.46347 + 2.06710i) q^{24} +(-0.795147 + 1.37724i) q^{26} +(-12.0914 + 6.98095i) q^{27} +(-0.00800160 - 0.0219842i) q^{28} +(7.09702 - 2.58310i) q^{29} +(-2.22993 + 3.86236i) q^{31} +(-0.984808 - 0.173648i) q^{32} +(4.46663 + 5.32312i) q^{33} +(-6.11281 - 5.12925i) q^{34} +(-6.89886 - 2.51098i) q^{36} -0.389132i q^{37} +(-3.60788 - 2.44606i) q^{38} -5.11413 q^{39} +(0.972920 + 5.51771i) q^{41} +(0.0483600 - 0.0576332i) q^{42} +(-6.23734 - 7.43337i) q^{43} +(-0.375222 + 2.12799i) q^{44} +(2.24033 + 3.88037i) q^{46} +(-1.46211 - 4.01711i) q^{47} +(-1.09988 - 3.02190i) q^{48} +(-3.49973 - 6.06170i) q^{49} +(4.45606 - 25.2716i) q^{51} +(-1.02222 - 1.21824i) q^{52} +(-2.43113 + 2.89731i) q^{53} +(-2.42446 - 13.7498i) q^{54} +0.0233951 q^{56} +(1.01111 - 13.9810i) q^{57} +7.55249i q^{58} +(-3.41426 - 1.24269i) q^{59} +(-8.84152 - 7.41891i) q^{61} +(-2.86675 - 3.41646i) q^{62} +(0.169148 + 0.0298254i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-6.52977 + 2.37664i) q^{66} +(-1.31913 - 3.62429i) q^{67} +(6.91062 - 3.98985i) q^{68} +(-7.20454 + 12.4786i) q^{69} +(-9.85813 + 8.27195i) q^{71} +(4.71909 - 5.62400i) q^{72} +(-1.87269 + 0.330206i) q^{73} +(0.365664 + 0.133091i) q^{74} +(3.53251 - 2.55369i) q^{76} -0.0505526i q^{77} +(1.74914 - 4.80571i) q^{78} +(1.65165 + 9.36698i) q^{79} +(17.5228 - 14.7034i) q^{81} +(-5.51771 - 0.972920i) q^{82} +(-2.27622 - 1.31417i) q^{83} +(0.0376174 + 0.0651553i) q^{84} +(9.11838 - 3.31882i) q^{86} +(-21.0337 + 12.1438i) q^{87} +(-1.87132 - 1.08041i) q^{88} +(-1.54115 + 8.74032i) q^{89} +(0.0285008 + 0.0239150i) q^{91} +(-4.41259 + 0.778059i) q^{92} +(4.90532 - 13.4773i) q^{93} +4.27492 q^{94} +3.21584 q^{96} +(3.81486 - 10.4812i) q^{97} +(6.89312 - 1.21544i) q^{98} +(-12.1524 - 10.1971i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 36q^{9} + O(q^{10}) \) \( 36q + 36q^{9} - 24q^{11} - 12q^{14} + 24q^{21} - 18q^{26} + 12q^{29} - 12q^{31} - 36q^{34} - 36q^{36} - 96q^{39} - 42q^{41} - 6q^{44} + 36q^{46} + 78q^{49} + 84q^{51} + 108q^{54} + 60q^{59} + 96q^{61} + 18q^{64} + 48q^{66} + 60q^{69} + 60q^{71} + 6q^{74} - 42q^{76} - 60q^{79} + 36q^{81} - 12q^{84} + 72q^{86} - 60q^{89} - 120q^{91} - 12q^{94} - 342q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{9}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.342020 + 0.939693i −0.241845 + 0.664463i
\(3\) −3.16698 + 0.558424i −1.82846 + 0.322406i −0.978783 0.204901i \(-0.934313\pi\)
−0.849675 + 0.527307i \(0.823202\pi\)
\(4\) −0.766044 0.642788i −0.383022 0.321394i
\(5\) 0 0
\(6\) 0.558424 3.16698i 0.227976 1.29291i
\(7\) 0.0202608 + 0.0116976i 0.00765785 + 0.00442126i 0.503824 0.863806i \(-0.331926\pi\)
−0.496166 + 0.868228i \(0.665259\pi\)
\(8\) 0.866025 0.500000i 0.306186 0.176777i
\(9\) 6.89886 2.51098i 2.29962 0.836993i
\(10\) 0 0
\(11\) −1.08041 1.87132i −0.325755 0.564225i 0.655910 0.754839i \(-0.272285\pi\)
−0.981665 + 0.190615i \(0.938952\pi\)
\(12\) 2.78500 + 1.60792i 0.803959 + 0.464166i
\(13\) 1.56613 + 0.276152i 0.434368 + 0.0765907i 0.386557 0.922266i \(-0.373664\pi\)
0.0478110 + 0.998856i \(0.484775\pi\)
\(14\) −0.0179217 + 0.0150381i −0.00478977 + 0.00401910i
\(15\) 0 0
\(16\) 0.173648 + 0.984808i 0.0434120 + 0.246202i
\(17\) −2.72922 + 7.49847i −0.661933 + 1.81865i −0.0939966 + 0.995573i \(0.529964\pi\)
−0.567936 + 0.823073i \(0.692258\pi\)
\(18\) 7.34161i 1.73043i
\(19\) −1.06458 + 4.22690i −0.244232 + 0.969717i
\(20\) 0 0
\(21\) −0.0706976 0.0257318i −0.0154275 0.00561515i
\(22\) 2.12799 0.375222i 0.453689 0.0799976i
\(23\) 2.88011 3.43239i 0.600545 0.715702i −0.377050 0.926193i \(-0.623062\pi\)
0.977596 + 0.210491i \(0.0675061\pi\)
\(24\) −2.46347 + 2.06710i −0.502855 + 0.421945i
\(25\) 0 0
\(26\) −0.795147 + 1.37724i −0.155941 + 0.270098i
\(27\) −12.0914 + 6.98095i −2.32698 + 1.34348i
\(28\) −0.00800160 0.0219842i −0.00151216 0.00415463i
\(29\) 7.09702 2.58310i 1.31788 0.479670i 0.415104 0.909774i \(-0.363745\pi\)
0.902780 + 0.430104i \(0.141523\pi\)
\(30\) 0 0
\(31\) −2.22993 + 3.86236i −0.400508 + 0.693700i −0.993787 0.111297i \(-0.964500\pi\)
0.593279 + 0.804997i \(0.297833\pi\)
\(32\) −0.984808 0.173648i −0.174091 0.0306970i
\(33\) 4.46663 + 5.32312i 0.777540 + 0.926636i
\(34\) −6.11281 5.12925i −1.04834 0.879660i
\(35\) 0 0
\(36\) −6.89886 2.51098i −1.14981 0.418496i
\(37\) 0.389132i 0.0639729i −0.999488 0.0319864i \(-0.989817\pi\)
0.999488 0.0319864i \(-0.0101833\pi\)
\(38\) −3.60788 2.44606i −0.585275 0.396804i
\(39\) −5.11413 −0.818916
\(40\) 0 0
\(41\) 0.972920 + 5.51771i 0.151945 + 0.861721i 0.961526 + 0.274713i \(0.0885830\pi\)
−0.809582 + 0.587007i \(0.800306\pi\)
\(42\) 0.0483600 0.0576332i 0.00746212 0.00889300i
\(43\) −6.23734 7.43337i −0.951185 1.13358i −0.990931 0.134369i \(-0.957099\pi\)
0.0397459 0.999210i \(-0.487345\pi\)
\(44\) −0.375222 + 2.12799i −0.0565668 + 0.320806i
\(45\) 0 0
\(46\) 2.24033 + 3.88037i 0.330319 + 0.572129i
\(47\) −1.46211 4.01711i −0.213271 0.585956i 0.786218 0.617950i \(-0.212037\pi\)
−0.999488 + 0.0319938i \(0.989814\pi\)
\(48\) −1.09988 3.02190i −0.158754 0.436173i
\(49\) −3.49973 6.06170i −0.499961 0.865958i
\(50\) 0 0
\(51\) 4.45606 25.2716i 0.623973 3.53873i
\(52\) −1.02222 1.21824i −0.141757 0.168939i
\(53\) −2.43113 + 2.89731i −0.333941 + 0.397976i −0.906719 0.421735i \(-0.861421\pi\)
0.572778 + 0.819711i \(0.305866\pi\)
\(54\) −2.42446 13.7498i −0.329927 1.87111i
\(55\) 0 0
\(56\) 0.0233951 0.00312630
\(57\) 1.01111 13.9810i 0.133925 1.85183i
\(58\) 7.55249i 0.991691i
\(59\) −3.41426 1.24269i −0.444499 0.161784i 0.110067 0.993924i \(-0.464893\pi\)
−0.554566 + 0.832140i \(0.687116\pi\)
\(60\) 0 0
\(61\) −8.84152 7.41891i −1.13204 0.949894i −0.132891 0.991131i \(-0.542426\pi\)
−0.999149 + 0.0412364i \(0.986870\pi\)
\(62\) −2.86675 3.41646i −0.364077 0.433890i
\(63\) 0.169148 + 0.0298254i 0.0213107 + 0.00375765i
\(64\) 0.500000 0.866025i 0.0625000 0.108253i
\(65\) 0 0
\(66\) −6.52977 + 2.37664i −0.803759 + 0.292544i
\(67\) −1.31913 3.62429i −0.161158 0.442778i 0.832662 0.553781i \(-0.186816\pi\)
−0.993820 + 0.111004i \(0.964593\pi\)
\(68\) 6.91062 3.98985i 0.838036 0.483840i
\(69\) −7.20454 + 12.4786i −0.867325 + 1.50225i
\(70\) 0 0
\(71\) −9.85813 + 8.27195i −1.16994 + 0.981700i −0.999993 0.00375214i \(-0.998806\pi\)
−0.169952 + 0.985452i \(0.554361\pi\)
\(72\) 4.71909 5.62400i 0.556151 0.662795i
\(73\) −1.87269 + 0.330206i −0.219182 + 0.0386477i −0.282161 0.959367i \(-0.591051\pi\)
0.0629785 + 0.998015i \(0.479940\pi\)
\(74\) 0.365664 + 0.133091i 0.0425076 + 0.0154715i
\(75\) 0 0
\(76\) 3.53251 2.55369i 0.405207 0.292928i
\(77\) 0.0505526i 0.00576100i
\(78\) 1.74914 4.80571i 0.198051 0.544139i
\(79\) 1.65165 + 9.36698i 0.185825 + 1.05387i 0.924891 + 0.380233i \(0.124156\pi\)
−0.739065 + 0.673634i \(0.764733\pi\)
\(80\) 0 0
\(81\) 17.5228 14.7034i 1.94698 1.63371i
\(82\) −5.51771 0.972920i −0.609329 0.107441i
\(83\) −2.27622 1.31417i −0.249847 0.144249i 0.369847 0.929093i \(-0.379410\pi\)
−0.619694 + 0.784843i \(0.712743\pi\)
\(84\) 0.0376174 + 0.0651553i 0.00410440 + 0.00710903i
\(85\) 0 0
\(86\) 9.11838 3.31882i 0.983260 0.357877i
\(87\) −21.0337 + 12.1438i −2.25505 + 1.30195i
\(88\) −1.87132 1.08041i −0.199484 0.115172i
\(89\) −1.54115 + 8.74032i −0.163362 + 0.926472i 0.787375 + 0.616474i \(0.211439\pi\)
−0.950737 + 0.309998i \(0.899672\pi\)
\(90\) 0 0
\(91\) 0.0285008 + 0.0239150i 0.00298769 + 0.00250697i
\(92\) −4.41259 + 0.778059i −0.460045 + 0.0811183i
\(93\) 4.90532 13.4773i 0.508658 1.39753i
\(94\) 4.27492 0.440924
\(95\) 0 0
\(96\) 3.21584 0.328215
\(97\) 3.81486 10.4812i 0.387340 1.06421i −0.580854 0.814008i \(-0.697281\pi\)
0.968194 0.250201i \(-0.0804966\pi\)
\(98\) 6.89312 1.21544i 0.696310 0.122778i
\(99\) −12.1524 10.1971i −1.22137 1.02485i
\(100\) 0 0
\(101\) −3.23809 + 18.3641i −0.322202 + 1.82730i 0.206449 + 0.978457i \(0.433809\pi\)
−0.528651 + 0.848840i \(0.677302\pi\)
\(102\) 22.2234 + 12.8307i 2.20045 + 1.27043i
\(103\) −3.06218 + 1.76795i −0.301726 + 0.174201i −0.643218 0.765683i \(-0.722401\pi\)
0.341492 + 0.939885i \(0.389068\pi\)
\(104\) 1.49439 0.543913i 0.146537 0.0533350i
\(105\) 0 0
\(106\) −1.89108 3.27545i −0.183678 0.318140i
\(107\) −4.84336 2.79632i −0.468226 0.270330i 0.247271 0.968946i \(-0.420466\pi\)
−0.715497 + 0.698616i \(0.753800\pi\)
\(108\) 13.7498 + 2.42446i 1.32307 + 0.233294i
\(109\) −7.21936 + 6.05777i −0.691490 + 0.580229i −0.919338 0.393468i \(-0.871275\pi\)
0.227849 + 0.973697i \(0.426831\pi\)
\(110\) 0 0
\(111\) 0.217301 + 1.23237i 0.0206253 + 0.116972i
\(112\) −0.00800160 + 0.0219842i −0.000756080 + 0.00207731i
\(113\) 5.69339i 0.535589i 0.963476 + 0.267795i \(0.0862948\pi\)
−0.963476 + 0.267795i \(0.913705\pi\)
\(114\) 12.7920 + 5.73191i 1.19808 + 0.536843i
\(115\) 0 0
\(116\) −7.09702 2.58310i −0.658942 0.239835i
\(117\) 11.4979 2.02740i 1.06299 0.187433i
\(118\) 2.33549 2.78333i 0.214999 0.256226i
\(119\) −0.143010 + 0.119999i −0.0131097 + 0.0110003i
\(120\) 0 0
\(121\) 3.16544 5.48269i 0.287767 0.498427i
\(122\) 9.99547 5.77089i 0.904948 0.522472i
\(123\) −6.16244 16.9312i −0.555649 1.52663i
\(124\) 4.19091 1.52536i 0.376354 0.136982i
\(125\) 0 0
\(126\) −0.0858789 + 0.148747i −0.00765070 + 0.0132514i
\(127\) 8.54334 + 1.50642i 0.758099 + 0.133673i 0.539320 0.842101i \(-0.318681\pi\)
0.218779 + 0.975774i \(0.429793\pi\)
\(128\) 0.642788 + 0.766044i 0.0568149 + 0.0677094i
\(129\) 23.9045 + 20.0583i 2.10468 + 1.76603i
\(130\) 0 0
\(131\) −19.4945 7.09542i −1.70324 0.619930i −0.707055 0.707159i \(-0.749977\pi\)
−0.996188 + 0.0872292i \(0.972199\pi\)
\(132\) 6.94884i 0.604818i
\(133\) −0.0710136 + 0.0731872i −0.00615766 + 0.00634613i
\(134\) 3.85689 0.333185
\(135\) 0 0
\(136\) 1.38566 + 7.85847i 0.118819 + 0.673858i
\(137\) −3.83636 + 4.57200i −0.327762 + 0.390612i −0.904610 0.426240i \(-0.859838\pi\)
0.576848 + 0.816852i \(0.304283\pi\)
\(138\) −9.26198 11.0380i −0.788432 0.939617i
\(139\) 2.44517 13.8672i 0.207397 1.17620i −0.686227 0.727387i \(-0.740734\pi\)
0.893624 0.448817i \(-0.148155\pi\)
\(140\) 0 0
\(141\) 6.87373 + 11.9056i 0.578872 + 1.00264i
\(142\) −4.40141 12.0928i −0.369358 1.01480i
\(143\) −1.17530 3.22910i −0.0982832 0.270031i
\(144\) 3.67080 + 6.35802i 0.305900 + 0.529835i
\(145\) 0 0
\(146\) 0.330206 1.87269i 0.0273281 0.154985i
\(147\) 14.4686 + 17.2430i 1.19335 + 1.42218i
\(148\) −0.250129 + 0.298092i −0.0205605 + 0.0245030i
\(149\) −1.22145 6.92721i −0.100065 0.567499i −0.993077 0.117465i \(-0.962523\pi\)
0.893012 0.450034i \(-0.148588\pi\)
\(150\) 0 0
\(151\) −14.0840 −1.14614 −0.573070 0.819507i \(-0.694248\pi\)
−0.573070 + 0.819507i \(0.694248\pi\)
\(152\) 1.19149 + 4.19289i 0.0966429 + 0.340088i
\(153\) 58.5838i 4.73622i
\(154\) 0.0475039 + 0.0172900i 0.00382797 + 0.00139327i
\(155\) 0 0
\(156\) 3.91765 + 3.28730i 0.313663 + 0.263195i
\(157\) 1.74085 + 2.07466i 0.138935 + 0.165576i 0.831025 0.556235i \(-0.187755\pi\)
−0.692090 + 0.721811i \(0.743310\pi\)
\(158\) −9.36698 1.65165i −0.745197 0.131398i
\(159\) 6.08141 10.5333i 0.482288 0.835346i
\(160\) 0 0
\(161\) 0.0985039 0.0358525i 0.00776319 0.00282557i
\(162\) 7.82350 + 21.4949i 0.614672 + 1.68880i
\(163\) −11.9479 + 6.89810i −0.935829 + 0.540301i −0.888650 0.458585i \(-0.848356\pi\)
−0.0471785 + 0.998886i \(0.515023\pi\)
\(164\) 2.80141 4.85219i 0.218754 0.378892i
\(165\) 0 0
\(166\) 2.01343 1.68947i 0.156273 0.131128i
\(167\) −15.5969 + 18.5877i −1.20692 + 1.43836i −0.339632 + 0.940558i \(0.610302\pi\)
−0.867293 + 0.497798i \(0.834142\pi\)
\(168\) −0.0740919 + 0.0130644i −0.00571631 + 0.00100794i
\(169\) −9.83949 3.58128i −0.756884 0.275483i
\(170\) 0 0
\(171\) 3.26925 + 31.8339i 0.250006 + 2.43440i
\(172\) 9.70358i 0.739891i
\(173\) 6.62267 18.1956i 0.503512 1.38339i −0.384311 0.923204i \(-0.625561\pi\)
0.887823 0.460184i \(-0.152217\pi\)
\(174\) −4.21749 23.9186i −0.319727 1.81326i
\(175\) 0 0
\(176\) 1.65528 1.38895i 0.124772 0.104696i
\(177\) 11.5068 + 2.02897i 0.864907 + 0.152506i
\(178\) −7.68611 4.43758i −0.576098 0.332610i
\(179\) 4.29621 + 7.44125i 0.321114 + 0.556185i 0.980718 0.195428i \(-0.0626095\pi\)
−0.659604 + 0.751613i \(0.729276\pi\)
\(180\) 0 0
\(181\) 3.94197 1.43476i 0.293005 0.106645i −0.191336 0.981525i \(-0.561282\pi\)
0.484340 + 0.874880i \(0.339060\pi\)
\(182\) −0.0322206 + 0.0186026i −0.00238835 + 0.00137891i
\(183\) 32.1438 + 18.5582i 2.37614 + 1.37186i
\(184\) 0.778059 4.41259i 0.0573593 0.325301i
\(185\) 0 0
\(186\) 10.9868 + 9.21899i 0.805589 + 0.675969i
\(187\) 16.9807 2.99416i 1.24175 0.218955i
\(188\) −1.46211 + 4.01711i −0.106635 + 0.292978i
\(189\) −0.326640 −0.0237596
\(190\) 0 0
\(191\) 18.8620 1.36481 0.682403 0.730976i \(-0.260935\pi\)
0.682403 + 0.730976i \(0.260935\pi\)
\(192\) −1.09988 + 3.02190i −0.0793771 + 0.218087i
\(193\) −17.5242 + 3.08999i −1.26142 + 0.222422i −0.764073 0.645130i \(-0.776803\pi\)
−0.497346 + 0.867552i \(0.665692\pi\)
\(194\) 8.54438 + 7.16959i 0.613451 + 0.514747i
\(195\) 0 0
\(196\) −1.21544 + 6.89312i −0.0868173 + 0.492365i
\(197\) −11.7025 6.75642i −0.833766 0.481375i 0.0213742 0.999772i \(-0.493196\pi\)
−0.855140 + 0.518396i \(0.826529\pi\)
\(198\) 13.7385 7.93194i 0.976354 0.563698i
\(199\) 6.59301 2.39966i 0.467366 0.170107i −0.0975926 0.995226i \(-0.531114\pi\)
0.564959 + 0.825119i \(0.308892\pi\)
\(200\) 0 0
\(201\) 6.20156 + 10.7414i 0.437425 + 0.757642i
\(202\) −16.1491 9.32370i −1.13625 0.656013i
\(203\) 0.174007 + 0.0306821i 0.0122129 + 0.00215346i
\(204\) −19.6578 + 16.4948i −1.37632 + 1.15487i
\(205\) 0 0
\(206\) −0.614003 3.48218i −0.0427796 0.242615i
\(207\) 11.2508 30.9114i 0.781988 2.14849i
\(208\) 1.59029i 0.110267i
\(209\) 9.06007 2.57460i 0.626698 0.178089i
\(210\) 0 0
\(211\) −6.68827 2.43433i −0.460440 0.167586i 0.101377 0.994848i \(-0.467675\pi\)
−0.561817 + 0.827262i \(0.689897\pi\)
\(212\) 3.72471 0.656766i 0.255814 0.0451069i
\(213\) 26.6013 31.7021i 1.82269 2.17219i
\(214\) 4.28421 3.59488i 0.292862 0.245741i
\(215\) 0 0
\(216\) −6.98095 + 12.0914i −0.474994 + 0.822713i
\(217\) −0.0903603 + 0.0521696i −0.00613406 + 0.00354150i
\(218\) −3.22327 8.85586i −0.218307 0.599795i
\(219\) 5.74639 2.09151i 0.388305 0.141331i
\(220\) 0 0
\(221\) −6.34504 + 10.9899i −0.426813 + 0.739263i
\(222\) −1.23237 0.217301i −0.0827115 0.0145843i
\(223\) 2.80259 + 3.34000i 0.187675 + 0.223663i 0.851675 0.524070i \(-0.175587\pi\)
−0.664000 + 0.747733i \(0.731142\pi\)
\(224\) −0.0179217 0.0150381i −0.00119744 0.00100477i
\(225\) 0 0
\(226\) −5.35004 1.94725i −0.355879 0.129529i
\(227\) 9.44623i 0.626969i 0.949593 + 0.313484i \(0.101496\pi\)
−0.949593 + 0.313484i \(0.898504\pi\)
\(228\) −9.76136 + 10.0601i −0.646462 + 0.666249i
\(229\) −22.8675 −1.51112 −0.755562 0.655077i \(-0.772636\pi\)
−0.755562 + 0.655077i \(0.772636\pi\)
\(230\) 0 0
\(231\) 0.0282298 + 0.160099i 0.00185738 + 0.0105337i
\(232\) 4.85465 5.78554i 0.318723 0.379840i
\(233\) 6.79851 + 8.10215i 0.445385 + 0.530790i 0.941295 0.337584i \(-0.109610\pi\)
−0.495910 + 0.868374i \(0.665165\pi\)
\(234\) −2.02740 + 11.4979i −0.132535 + 0.751644i
\(235\) 0 0
\(236\) 1.81669 + 3.14660i 0.118256 + 0.204826i
\(237\) −10.4615 28.7427i −0.679547 1.86704i
\(238\) −0.0638504 0.175427i −0.00413880 0.0113713i
\(239\) 8.67636 + 15.0279i 0.561227 + 0.972074i 0.997390 + 0.0722058i \(0.0230038\pi\)
−0.436163 + 0.899868i \(0.643663\pi\)
\(240\) 0 0
\(241\) −0.0833347 + 0.472614i −0.00536806 + 0.0304438i −0.987374 0.158406i \(-0.949365\pi\)
0.982006 + 0.188849i \(0.0604758\pi\)
\(242\) 4.06940 + 4.84973i 0.261591 + 0.311752i
\(243\) −20.3600 + 24.2641i −1.30610 + 1.55655i
\(244\) 2.00421 + 11.3664i 0.128306 + 0.727661i
\(245\) 0 0
\(246\) 18.0178 1.14877
\(247\) −2.83454 + 6.32590i −0.180358 + 0.402508i
\(248\) 4.45987i 0.283202i
\(249\) 7.94260 + 2.89087i 0.503342 + 0.183202i
\(250\) 0 0
\(251\) 4.56913 + 3.83396i 0.288401 + 0.241997i 0.775497 0.631351i \(-0.217499\pi\)
−0.487096 + 0.873348i \(0.661944\pi\)
\(252\) −0.110404 0.131574i −0.00695478 0.00828839i
\(253\) −9.53480 1.68124i −0.599448 0.105699i
\(254\) −4.33757 + 7.51289i −0.272163 + 0.471400i
\(255\) 0 0
\(256\) −0.939693 + 0.342020i −0.0587308 + 0.0213763i
\(257\) 4.62683 + 12.7121i 0.288614 + 0.792959i 0.996261 + 0.0863936i \(0.0275343\pi\)
−0.707648 + 0.706566i \(0.750244\pi\)
\(258\) −27.0244 + 15.6026i −1.68247 + 0.971373i
\(259\) 0.00455189 0.00788411i 0.000282841 0.000489895i
\(260\) 0 0
\(261\) 42.4752 35.6409i 2.62915 2.20612i
\(262\) 13.3350 15.8921i 0.823841 0.981815i
\(263\) −17.3493 + 3.05915i −1.06980 + 0.188635i −0.680703 0.732560i \(-0.738326\pi\)
−0.389101 + 0.921195i \(0.627214\pi\)
\(264\) 6.52977 + 2.37664i 0.401880 + 0.146272i
\(265\) 0 0
\(266\) −0.0444853 0.0917624i −0.00272757 0.00562632i
\(267\) 28.5410i 1.74668i
\(268\) −1.31913 + 3.62429i −0.0805789 + 0.221389i
\(269\) 0.447725 + 2.53918i 0.0272983 + 0.154816i 0.995410 0.0957028i \(-0.0305098\pi\)
−0.968112 + 0.250519i \(0.919399\pi\)
\(270\) 0 0
\(271\) −8.49966 + 7.13206i −0.516318 + 0.433242i −0.863346 0.504613i \(-0.831635\pi\)
0.347028 + 0.937855i \(0.387191\pi\)
\(272\) −7.85847 1.38566i −0.476490 0.0840180i
\(273\) −0.103616 0.0598228i −0.00627113 0.00362064i
\(274\) −2.98416 5.16871i −0.180280 0.312253i
\(275\) 0 0
\(276\) 13.5401 4.92820i 0.815019 0.296643i
\(277\) −2.55932 + 1.47762i −0.153774 + 0.0887817i −0.574913 0.818215i \(-0.694964\pi\)
0.421138 + 0.906996i \(0.361631\pi\)
\(278\) 12.1947 + 7.04059i 0.731387 + 0.422266i
\(279\) −5.68569 + 32.2452i −0.340394 + 1.93047i
\(280\) 0 0
\(281\) 10.6181 + 8.90966i 0.633424 + 0.531506i 0.901991 0.431755i \(-0.142106\pi\)
−0.268567 + 0.963261i \(0.586550\pi\)
\(282\) −13.5386 + 2.38722i −0.806212 + 0.142157i
\(283\) 1.58707 4.36045i 0.0943418 0.259202i −0.883542 0.468353i \(-0.844848\pi\)
0.977883 + 0.209151i \(0.0670699\pi\)
\(284\) 12.8689 0.763627
\(285\) 0 0
\(286\) 3.43634 0.203195
\(287\) −0.0448316 + 0.123174i −0.00264632 + 0.00727071i
\(288\) −7.23007 + 1.27486i −0.426036 + 0.0751217i
\(289\) −35.7556 30.0025i −2.10327 1.76485i
\(290\) 0 0
\(291\) −6.22861 + 35.3242i −0.365128 + 2.07074i
\(292\) 1.64682 + 0.950791i 0.0963728 + 0.0556409i
\(293\) −10.2765 + 5.93313i −0.600358 + 0.346617i −0.769182 0.639029i \(-0.779336\pi\)
0.168824 + 0.985646i \(0.446003\pi\)
\(294\) −21.1516 + 7.69857i −1.23359 + 0.448989i
\(295\) 0 0
\(296\) −0.194566 0.336998i −0.0113089 0.0195876i
\(297\) 26.1272 + 15.0846i 1.51606 + 0.875295i
\(298\) 6.92721 + 1.22145i 0.401282 + 0.0707569i
\(299\) 5.45851 4.58023i 0.315674 0.264882i
\(300\) 0 0
\(301\) −0.0394210 0.223567i −0.00227219 0.0128862i
\(302\) 4.81701 13.2346i 0.277188 0.761567i
\(303\) 59.9670i 3.44501i
\(304\) −4.34754 0.314416i −0.249349 0.0180330i
\(305\) 0 0
\(306\) −55.0508 20.0369i −3.14704 1.14543i
\(307\) −10.2836 + 1.81328i −0.586918 + 0.103489i −0.459218 0.888323i \(-0.651870\pi\)
−0.127699 + 0.991813i \(0.540759\pi\)
\(308\) −0.0324946 + 0.0387255i −0.00185155 + 0.00220659i
\(309\) 8.71060 7.30906i 0.495529 0.415798i
\(310\) 0 0
\(311\) 7.33307 12.7012i 0.415820 0.720222i −0.579694 0.814834i \(-0.696828\pi\)
0.995514 + 0.0946125i \(0.0301612\pi\)
\(312\) −4.42897 + 2.55706i −0.250741 + 0.144765i
\(313\) −7.34588 20.1826i −0.415214 1.14079i −0.954381 0.298592i \(-0.903483\pi\)
0.539167 0.842199i \(-0.318739\pi\)
\(314\) −2.54495 + 0.926285i −0.143620 + 0.0522733i
\(315\) 0 0
\(316\) 4.75574 8.23718i 0.267531 0.463378i
\(317\) 11.6370 + 2.05192i 0.653599 + 0.115247i 0.490608 0.871381i \(-0.336775\pi\)
0.162991 + 0.986628i \(0.447886\pi\)
\(318\) 7.81812 + 9.31727i 0.438418 + 0.522486i
\(319\) −12.5015 10.4900i −0.699950 0.587327i
\(320\) 0 0
\(321\) 16.9004 + 6.15123i 0.943287 + 0.343328i
\(322\) 0.104826i 0.00584170i
\(323\) −28.7898 19.5189i −1.60191 1.08606i
\(324\) −22.8744 −1.27080
\(325\) 0 0
\(326\) −2.39569 13.5866i −0.132685 0.752493i
\(327\) 19.4808 23.2163i 1.07729 1.28386i
\(328\) 3.60143 + 4.29201i 0.198856 + 0.236987i
\(329\) 0.0173669 0.0984928i 0.000957471 0.00543009i
\(330\) 0 0
\(331\) −8.88073 15.3819i −0.488129 0.845464i 0.511778 0.859118i \(-0.328987\pi\)
−0.999907 + 0.0136535i \(0.995654\pi\)
\(332\) 0.898948 + 2.46984i 0.0493362 + 0.135550i
\(333\) −0.977102 2.68456i −0.0535448 0.147113i
\(334\) −12.1322 21.0137i −0.663847 1.14982i
\(335\) 0 0
\(336\) 0.0130644 0.0740919i 0.000712721 0.00404204i
\(337\) 1.53351 + 1.82756i 0.0835354 + 0.0995537i 0.806193 0.591652i \(-0.201524\pi\)
−0.722658 + 0.691206i \(0.757080\pi\)
\(338\) 6.73060 8.02122i 0.366097 0.436297i
\(339\) −3.17933 18.0309i −0.172677 0.979302i
\(340\) 0 0
\(341\) 9.63696 0.521871
\(342\) −31.0322 7.81574i −1.67803 0.422627i
\(343\) 0.327519i 0.0176843i
\(344\) −9.11838 3.31882i −0.491630 0.178939i
\(345\) 0 0
\(346\) 14.8332 + 12.4465i 0.797438 + 0.669130i
\(347\) 9.89984 + 11.7982i 0.531451 + 0.633359i 0.963249 0.268612i \(-0.0865649\pi\)
−0.431797 + 0.901971i \(0.642120\pi\)
\(348\) 23.9186 + 4.21749i 1.28217 + 0.226081i
\(349\) 4.92259 8.52618i 0.263500 0.456396i −0.703669 0.710528i \(-0.748456\pi\)
0.967170 + 0.254132i \(0.0817897\pi\)
\(350\) 0 0
\(351\) −20.8645 + 7.59406i −1.11366 + 0.405341i
\(352\) 0.739043 + 2.03050i 0.0393911 + 0.108226i
\(353\) 7.37302 4.25682i 0.392426 0.226567i −0.290785 0.956789i \(-0.593916\pi\)
0.683211 + 0.730221i \(0.260583\pi\)
\(354\) −5.84218 + 10.1189i −0.310508 + 0.537816i
\(355\) 0 0
\(356\) 6.79876 5.70484i 0.360334 0.302356i
\(357\) 0.385899 0.459896i 0.0204239 0.0243403i
\(358\) −8.46188 + 1.49206i −0.447224 + 0.0788577i
\(359\) 29.6177 + 10.7800i 1.56317 + 0.568946i 0.971459 0.237208i \(-0.0762323\pi\)
0.591706 + 0.806154i \(0.298455\pi\)
\(360\) 0 0
\(361\) −16.7333 8.99976i −0.880702 0.473672i
\(362\) 4.19496i 0.220482i
\(363\) −6.96320 + 19.1312i −0.365473 + 1.00413i
\(364\) −0.00646060 0.0366399i −0.000338628 0.00192045i
\(365\) 0 0
\(366\) −28.4329 + 23.8580i −1.48621 + 1.24708i
\(367\) 6.86889 + 1.21117i 0.358553 + 0.0632226i 0.350023 0.936741i \(-0.386174\pi\)
0.00853004 + 0.999964i \(0.497285\pi\)
\(368\) 3.88037 + 2.24033i 0.202278 + 0.116785i
\(369\) 20.5669 + 35.6229i 1.07067 + 1.85445i
\(370\) 0 0
\(371\) −0.0831479 + 0.0302634i −0.00431683 + 0.00157120i
\(372\) −12.4207 + 7.17110i −0.643984 + 0.371804i
\(373\) 10.4397 + 6.02737i 0.540548 + 0.312085i 0.745301 0.666728i \(-0.232306\pi\)
−0.204753 + 0.978814i \(0.565639\pi\)
\(374\) −2.99416 + 16.9807i −0.154824 + 0.878052i
\(375\) 0 0
\(376\) −3.27478 2.74787i −0.168884 0.141710i
\(377\) 11.8282 2.08563i 0.609184 0.107416i
\(378\) 0.111718 0.306941i 0.00574613 0.0157874i
\(379\) 6.82285 0.350466 0.175233 0.984527i \(-0.443932\pi\)
0.175233 + 0.984527i \(0.443932\pi\)
\(380\) 0 0
\(381\) −27.8978 −1.42925
\(382\) −6.45118 + 17.7245i −0.330071 + 0.906863i
\(383\) 10.6626 1.88011i 0.544834 0.0960690i 0.105545 0.994415i \(-0.466341\pi\)
0.439290 + 0.898346i \(0.355230\pi\)
\(384\) −2.46347 2.06710i −0.125714 0.105486i
\(385\) 0 0
\(386\) 3.08999 17.5242i 0.157276 0.891958i
\(387\) −61.6955 35.6199i −3.13616 1.81066i
\(388\) −9.65956 + 5.57695i −0.490390 + 0.283127i
\(389\) −7.07236 + 2.57413i −0.358583 + 0.130513i −0.515028 0.857173i \(-0.672219\pi\)
0.156446 + 0.987687i \(0.449996\pi\)
\(390\) 0 0
\(391\) 17.8772 + 30.9642i 0.904088 + 1.56593i
\(392\) −6.06170 3.49973i −0.306162 0.176763i
\(393\) 65.7010 + 11.5849i 3.31418 + 0.584379i
\(394\) 10.3514 8.68589i 0.521498 0.437589i
\(395\) 0 0
\(396\) 2.75473 + 15.6229i 0.138431 + 0.785078i
\(397\) −1.69258 + 4.65031i −0.0849479 + 0.233393i −0.974892 0.222676i \(-0.928521\pi\)
0.889944 + 0.456069i \(0.150743\pi\)
\(398\) 7.01614i 0.351687i
\(399\) 0.184029 0.271438i 0.00921299 0.0135889i
\(400\) 0 0
\(401\) −18.6833 6.80015i −0.932998 0.339583i −0.169601 0.985513i \(-0.554248\pi\)
−0.763397 + 0.645929i \(0.776470\pi\)
\(402\) −12.2147 + 2.15378i −0.609214 + 0.107421i
\(403\) −4.55897 + 5.43317i −0.227099 + 0.270646i
\(404\) 14.2847 11.9863i 0.710692 0.596342i
\(405\) 0 0
\(406\) −0.0883457 + 0.153019i −0.00438452 + 0.00759422i
\(407\) −0.728191 + 0.420421i −0.0360951 + 0.0208395i
\(408\) −8.77672 24.1138i −0.434512 1.19381i
\(409\) 12.1132 4.40884i 0.598958 0.218003i −0.0247068 0.999695i \(-0.507865\pi\)
0.623665 + 0.781692i \(0.285643\pi\)
\(410\) 0 0
\(411\) 9.59657 16.6217i 0.473364 0.819890i
\(412\) 3.48218 + 0.614003i 0.171555 + 0.0302497i
\(413\) −0.0546391 0.0651163i −0.00268861 0.00320416i
\(414\) 25.1992 + 21.1447i 1.23848 + 1.03920i
\(415\) 0 0
\(416\) −1.49439 0.543913i −0.0732684 0.0266675i
\(417\) 45.2828i 2.21751i
\(418\) −0.679394 + 9.39425i −0.0332303 + 0.459488i
\(419\) −4.48425 −0.219070 −0.109535 0.993983i \(-0.534936\pi\)
−0.109535 + 0.993983i \(0.534936\pi\)
\(420\) 0 0
\(421\) −3.74698 21.2502i −0.182616 1.03567i −0.928980 0.370131i \(-0.879313\pi\)
0.746363 0.665539i \(-0.231798\pi\)
\(422\) 4.57505 5.45233i 0.222710 0.265415i
\(423\) −20.1738 24.0421i −0.980882 1.16897i
\(424\) −0.656766 + 3.72471i −0.0318954 + 0.180888i
\(425\) 0 0
\(426\) 20.6921 + 35.8398i 1.00254 + 1.73644i
\(427\) −0.0923527 0.253737i −0.00446926 0.0122792i
\(428\) 1.91279 + 5.25536i 0.0924584 + 0.254027i
\(429\) 5.52535 + 9.57018i 0.266766 + 0.462053i
\(430\) 0 0
\(431\) 2.06827 11.7298i 0.0996252 0.565003i −0.893606 0.448852i \(-0.851833\pi\)
0.993232 0.116151i \(-0.0370557\pi\)
\(432\) −8.97454 10.6954i −0.431788 0.514585i
\(433\) 14.2251 16.9528i 0.683615 0.814701i −0.306952 0.951725i \(-0.599309\pi\)
0.990568 + 0.137024i \(0.0437537\pi\)
\(434\) −0.0181183 0.102754i −0.000869706 0.00493235i
\(435\) 0 0
\(436\) 9.42421 0.451338
\(437\) 11.4422 + 15.8280i 0.547356 + 0.757156i
\(438\) 6.11518i 0.292195i
\(439\) −6.47904 2.35818i −0.309228 0.112550i 0.182745 0.983160i \(-0.441502\pi\)
−0.491973 + 0.870611i \(0.663724\pi\)
\(440\) 0 0
\(441\) −39.3649 33.0311i −1.87452 1.57291i
\(442\) −8.15702 9.72116i −0.387990 0.462389i
\(443\) 1.52212 + 0.268390i 0.0723180 + 0.0127516i 0.209690 0.977768i \(-0.432754\pi\)
−0.137372 + 0.990520i \(0.543866\pi\)
\(444\) 0.625692 1.08373i 0.0296940 0.0514316i
\(445\) 0 0
\(446\) −4.09711 + 1.49123i −0.194004 + 0.0706117i
\(447\) 7.73664 + 21.2562i 0.365931 + 1.00539i
\(448\) 0.0202608 0.0116976i 0.000957231 0.000552658i
\(449\) 2.95993 5.12674i 0.139688 0.241946i −0.787691 0.616071i \(-0.788724\pi\)
0.927378 + 0.374125i \(0.122057\pi\)
\(450\) 0 0
\(451\) 9.27425 7.78202i 0.436708 0.366441i
\(452\) 3.65964 4.36139i 0.172135 0.205143i
\(453\) 44.6038 7.86485i 2.09567 0.369523i
\(454\) −8.87656 3.23080i −0.416597 0.151629i
\(455\) 0 0
\(456\) −6.11485 12.6135i −0.286354 0.590679i
\(457\) 29.5382i 1.38174i 0.722979 + 0.690870i \(0.242772\pi\)
−0.722979 + 0.690870i \(0.757228\pi\)
\(458\) 7.82113 21.4884i 0.365458 1.00409i
\(459\) −19.3465 109.719i −0.903015 5.12125i
\(460\) 0 0
\(461\) 23.3287 19.5751i 1.08652 0.911702i 0.0900776 0.995935i \(-0.471288\pi\)
0.996446 + 0.0842331i \(0.0268440\pi\)
\(462\) −0.160099 0.0282298i −0.00744848 0.00131337i
\(463\) 33.6554 + 19.4309i 1.56410 + 0.903033i 0.996835 + 0.0794963i \(0.0253312\pi\)
0.567263 + 0.823536i \(0.308002\pi\)
\(464\) 3.77625 + 6.54065i 0.175308 + 0.303642i
\(465\) 0 0
\(466\) −9.93876 + 3.61741i −0.460404 + 0.167573i
\(467\) 24.7927 14.3141i 1.14727 0.662377i 0.199050 0.979989i \(-0.436214\pi\)
0.948221 + 0.317612i \(0.102881\pi\)
\(468\) −10.1111 5.83766i −0.467387 0.269846i
\(469\) 0.0156687 0.0888615i 0.000723513 0.00410324i
\(470\) 0 0
\(471\) −6.67177 5.59828i −0.307419 0.257955i
\(472\) −3.57818 + 0.630930i −0.164699 + 0.0290409i
\(473\) −7.17136 + 19.7032i −0.329740 + 0.905952i
\(474\) 30.5874 1.40492
\(475\) 0 0
\(476\) 0.186686 0.00855674
\(477\) −9.49693 + 26.0926i −0.434835 + 1.19470i
\(478\) −17.0891 + 3.01327i −0.781637 + 0.137824i
\(479\) 12.7889 + 10.7312i 0.584340 + 0.490320i 0.886369 0.462979i \(-0.153219\pi\)
−0.302029 + 0.953299i \(0.597664\pi\)
\(480\) 0 0
\(481\) 0.107459 0.609433i 0.00489973 0.0277877i
\(482\) −0.415610 0.239953i −0.0189305 0.0109295i
\(483\) −0.291939 + 0.168551i −0.0132837 + 0.00766934i
\(484\) −5.94907 + 2.16529i −0.270412 + 0.0984221i
\(485\) 0 0
\(486\) −15.8373 27.4310i −0.718394 1.24430i
\(487\) −16.7864 9.69165i −0.760666 0.439171i 0.0688690 0.997626i \(-0.478061\pi\)
−0.829535 + 0.558455i \(0.811394\pi\)
\(488\) −11.3664 2.00421i −0.514534 0.0907263i
\(489\) 33.9866 28.5181i 1.53693 1.28963i
\(490\) 0 0
\(491\) 6.30923 + 35.7814i 0.284731 + 1.61479i 0.706243 + 0.707970i \(0.250389\pi\)
−0.421511 + 0.906823i \(0.638500\pi\)
\(492\) −6.16244 + 16.9312i −0.277824 + 0.763316i
\(493\) 60.2666i 2.71427i
\(494\) −4.97493 4.82719i −0.223833 0.217185i
\(495\) 0 0
\(496\) −4.19091 1.52536i −0.188177 0.0684909i
\(497\) −0.296495 + 0.0522800i −0.0132996 + 0.00234508i
\(498\) −5.43306 + 6.47487i −0.243461 + 0.290146i
\(499\) 5.94585 4.98916i 0.266173 0.223346i −0.499926 0.866068i \(-0.666640\pi\)
0.766099 + 0.642722i \(0.222195\pi\)
\(500\) 0 0
\(501\) 39.0153 67.5765i 1.74308 3.01909i
\(502\) −5.16548 + 2.98229i −0.230546 + 0.133106i
\(503\) 0.217326 + 0.597098i 0.00969008 + 0.0266233i 0.944443 0.328674i \(-0.106602\pi\)
−0.934753 + 0.355297i \(0.884380\pi\)
\(504\) 0.161399 0.0587446i 0.00718930 0.00261669i
\(505\) 0 0
\(506\) 4.84095 8.38477i 0.215206 0.372748i
\(507\) 33.1613 + 5.84724i 1.47275 + 0.259685i
\(508\) −5.57627 6.64554i −0.247407 0.294848i
\(509\) −20.1192 16.8820i −0.891767 0.748282i 0.0767966 0.997047i \(-0.475531\pi\)
−0.968564 + 0.248765i \(0.919975\pi\)
\(510\) 0 0
\(511\) −0.0418048 0.0152157i −0.00184934 0.000673103i
\(512\) 1.00000i 0.0441942i
\(513\) −16.6355 58.5408i −0.734476 2.58464i
\(514\) −13.5279 −0.596692
\(515\) 0 0
\(516\) −5.41871 30.7311i −0.238546 1.35286i
\(517\) −5.93764 + 7.07620i −0.261137 + 0.311211i
\(518\) 0.00585180 + 0.00697390i 0.000257113 + 0.000306416i
\(519\) −10.8130 + 61.3235i −0.474637 + 2.69180i
\(520\) 0 0
\(521\) −20.1453 34.8927i −0.882583 1.52868i −0.848459 0.529262i \(-0.822469\pi\)
−0.0341245 0.999418i \(-0.510864\pi\)
\(522\) 18.9641 + 52.1035i 0.830038 + 2.28051i
\(523\) 5.72897 + 15.7402i 0.250510 + 0.688271i 0.999665 + 0.0258764i \(0.00823762\pi\)
−0.749155 + 0.662395i \(0.769540\pi\)
\(524\) 10.3728 + 17.9662i 0.453138 + 0.784859i
\(525\) 0 0
\(526\) 3.05915 17.3493i 0.133385 0.756466i
\(527\) −22.8758 27.2623i −0.996485 1.18756i
\(528\) −4.46663 + 5.32312i −0.194385 + 0.231659i
\(529\) 0.507688 + 2.87924i 0.0220734 + 0.125184i
\(530\) 0 0
\(531\) −26.6748 −1.15759
\(532\) 0.101443 0.0104179i 0.00439813 0.000451675i
\(533\) 8.91014i 0.385941i
\(534\) 26.8198 + 9.76161i 1.16061 + 0.422426i
\(535\) 0 0
\(536\) −2.95455 2.47916i −0.127617 0.107083i
\(537\) −17.7614 21.1672i −0.766461 0.913432i
\(538\) −2.53918 0.447725i −0.109472 0.0193028i
\(539\) −7.56227 + 13.0982i −0.325730 + 0.564181i
\(540\) 0 0
\(541\) −28.7784 + 10.4745i −1.23728 + 0.450334i −0.876085 0.482156i \(-0.839854\pi\)
−0.361196 + 0.932490i \(0.617632\pi\)
\(542\) −3.79489 10.4264i −0.163005 0.447851i
\(543\) −11.6830 + 6.74515i −0.501363 + 0.289462i
\(544\) 3.98985 6.91062i 0.171063 0.296291i
\(545\) 0 0
\(546\) 0.0916539 0.0769067i 0.00392242 0.00329130i
\(547\) 0.00515474 0.00614318i 0.000220401 0.000262663i −0.765934 0.642919i \(-0.777723\pi\)
0.766155 + 0.642656i \(0.222168\pi\)
\(548\) 5.87764 1.03639i 0.251081 0.0442723i
\(549\) −79.6251 28.9812i −3.39831 1.23689i
\(550\) 0 0
\(551\) 3.36316 + 32.7483i 0.143275 + 1.39512i
\(552\) 14.4091i 0.613291i
\(553\) −0.0761070 + 0.209102i −0.00323640 + 0.00889194i
\(554\) −0.513173 2.91035i −0.0218026 0.123649i
\(555\) 0 0
\(556\) −10.7868 + 9.05120i −0.457462 + 0.383856i
\(557\) 6.59116 + 1.16220i 0.279276 + 0.0492440i 0.311532 0.950236i \(-0.399158\pi\)
−0.0322555 + 0.999480i \(0.510269\pi\)
\(558\) −28.3559 16.3713i −1.20040 0.693052i
\(559\) −7.71578 13.3641i −0.326343 0.565242i
\(560\) 0 0
\(561\) −52.1056 + 18.9649i −2.19990 + 0.800698i
\(562\) −12.0040 + 6.93049i −0.506356 + 0.292345i
\(563\) 5.72191 + 3.30354i 0.241150 + 0.139228i 0.615705 0.787977i \(-0.288871\pi\)
−0.374555 + 0.927205i \(0.622205\pi\)
\(564\) 2.38722 13.5386i 0.100520 0.570078i
\(565\) 0 0
\(566\) 3.55467 + 2.98272i 0.149414 + 0.125373i
\(567\) 0.527019 0.0929276i 0.0221327 0.00390259i
\(568\) −4.40141 + 12.0928i −0.184679 + 0.507402i
\(569\) 18.2452 0.764879 0.382440 0.923980i \(-0.375084\pi\)
0.382440 + 0.923980i \(0.375084\pi\)
\(570\) 0 0
\(571\) −4.61851 −0.193279 −0.0966393 0.995319i \(-0.530809\pi\)
−0.0966393 + 0.995319i \(0.530809\pi\)
\(572\) −1.17530 + 3.22910i −0.0491416 + 0.135015i
\(573\) −59.7356 + 10.5330i −2.49549 + 0.440022i
\(574\) −0.100412 0.0842558i −0.00419112 0.00351677i
\(575\) 0 0
\(576\) 1.27486 7.23007i 0.0531190 0.301253i
\(577\) 34.9245 + 20.1637i 1.45393 + 0.839424i 0.998701 0.0509529i \(-0.0162258\pi\)
0.455224 + 0.890377i \(0.349559\pi\)
\(578\) 40.4223 23.3378i 1.68135 0.970725i
\(579\) 53.7733 19.5719i 2.23474 0.813379i
\(580\) 0 0
\(581\) −0.0307453 0.0532524i −0.00127553 0.00220928i
\(582\) −31.0636 17.9346i −1.28763 0.743412i
\(583\) 8.04841 + 1.41915i 0.333331 + 0.0587752i
\(584\) −1.45670 + 1.22231i −0.0602785 + 0.0505797i
\(585\) 0 0
\(586\) −2.06055 11.6860i −0.0851207 0.482743i
\(587\) 5.21623 14.3315i 0.215297 0.591523i −0.784286 0.620399i \(-0.786971\pi\)
0.999583 + 0.0288761i \(0.00919283\pi\)
\(588\) 22.5091i 0.928260i
\(589\) −13.9518 13.5375i −0.574876 0.557803i
\(590\) 0 0
\(591\) 40.8344 + 14.8625i 1.67970 + 0.611363i
\(592\) 0.383220 0.0675720i 0.0157502 0.00277719i
\(593\) −25.7487 + 30.6860i −1.05737 + 1.26012i −0.0929726 + 0.995669i \(0.529637\pi\)
−0.964398 + 0.264456i \(0.914808\pi\)
\(594\) −23.1109 + 19.3923i −0.948251 + 0.795677i
\(595\) 0 0
\(596\) −3.51704 + 6.09168i −0.144063 + 0.249525i
\(597\) −19.5399 + 11.2814i −0.799716 + 0.461716i
\(598\) 2.43709 + 6.69585i 0.0996600 + 0.273814i
\(599\) −25.5138 + 9.28628i −1.04247 + 0.379427i −0.805815 0.592167i \(-0.798272\pi\)
−0.236652 + 0.971594i \(0.576050\pi\)
\(600\) 0 0
\(601\) 12.9663 22.4583i 0.528907 0.916094i −0.470525 0.882387i \(-0.655935\pi\)
0.999432 0.0337070i \(-0.0107313\pi\)
\(602\) 0.223567 + 0.0394210i 0.00911193 + 0.00160668i
\(603\) −18.2010 21.6911i −0.741203 0.883332i
\(604\) 10.7890 + 9.05302i 0.438997 + 0.368362i
\(605\) 0 0
\(606\) 56.3506 + 20.5099i 2.28908 + 0.833159i
\(607\) 15.2583i 0.619316i −0.950848 0.309658i \(-0.899785\pi\)
0.950848 0.309658i \(-0.100215\pi\)
\(608\) 1.78240 3.97782i 0.0722859 0.161322i
\(609\) −0.568211 −0.0230251
\(610\) 0 0
\(611\) −1.18053 6.69510i −0.0477590 0.270855i
\(612\) 37.6570 44.8778i 1.52219 1.81408i
\(613\) 3.03440 + 3.61626i 0.122558 + 0.146059i 0.823835 0.566830i \(-0.191831\pi\)
−0.701276 + 0.712890i \(0.747386\pi\)
\(614\) 1.81328 10.2836i 0.0731781 0.415013i
\(615\) 0 0
\(616\) −0.0252763 0.0437798i −0.00101841 0.00176394i
\(617\) −10.3569 28.4553i −0.416953 1.14557i −0.953420 0.301647i \(-0.902463\pi\)
0.536467 0.843922i \(-0.319759\pi\)
\(618\) 3.88907 + 10.6851i 0.156441 + 0.429819i
\(619\) −2.84795 4.93279i −0.114469 0.198266i 0.803099 0.595846i \(-0.203183\pi\)
−0.917567 + 0.397581i \(0.869850\pi\)
\(620\) 0 0
\(621\) −10.8632 + 61.6082i −0.435925 + 2.47225i
\(622\) 9.42721 + 11.2349i 0.377997 + 0.450479i
\(623\) −0.133465 + 0.159058i −0.00534718 + 0.00637252i
\(624\) −0.888059 5.03643i −0.0355508 0.201619i
\(625\) 0 0
\(626\) 21.4779 0.858430
\(627\) −27.2554 + 13.2131i −1.08847 + 0.527679i
\(628\) 2.70828i 0.108072i
\(629\) 2.91789 + 1.06203i 0.116344 + 0.0423457i
\(630\) 0 0
\(631\) −32.4485 27.2275i −1.29175 1.08391i −0.991508 0.130048i \(-0.958487\pi\)
−0.300246 0.953862i \(-0.597069\pi\)
\(632\) 6.11386 + 7.28621i 0.243196 + 0.289830i
\(633\) 22.5410 + 3.97459i 0.895925 + 0.157976i
\(634\) −5.90826 + 10.2334i −0.234647 + 0.406420i
\(635\) 0 0
\(636\) −11.4293 + 4.15993i −0.453202 + 0.164952i
\(637\) −3.80709 10.4599i −0.150842 0.414436i
\(638\) 14.1331 8.15977i 0.559537 0.323049i
\(639\) −47.2391 + 81.8206i −1.86875 + 3.23677i
\(640\) 0 0
\(641\) −20.8636 + 17.5066i −0.824062 + 0.691470i −0.953920 0.300063i \(-0.902992\pi\)
0.129858 + 0.991533i \(0.458548\pi\)
\(642\) −11.5605 + 13.7773i −0.456258 + 0.543747i
\(643\) −3.45211 + 0.608700i −0.136138 + 0.0240048i −0.241302 0.970450i \(-0.577574\pi\)
0.105164 + 0.994455i \(0.466463\pi\)
\(644\) −0.0985039 0.0358525i −0.00388160 0.00141279i
\(645\) 0 0
\(646\) 28.1884 20.3777i 1.10906 0.801750i
\(647\) 44.9855i 1.76856i 0.466956 + 0.884280i \(0.345351\pi\)
−0.466956 + 0.884280i \(0.654649\pi\)
\(648\) 7.82350 21.4949i 0.307336 0.844399i
\(649\) 1.36332 + 7.73179i 0.0535151 + 0.303499i
\(650\) 0 0
\(651\) 0.257037 0.215679i 0.0100741 0.00845314i
\(652\) 13.5866 + 2.39569i 0.532093 + 0.0938223i
\(653\) 13.7877 + 7.96033i 0.539555 + 0.311512i 0.744898 0.667178i \(-0.232498\pi\)
−0.205344 + 0.978690i \(0.565831\pi\)
\(654\) 15.1534 + 26.2464i 0.592543 + 1.02632i
\(655\) 0 0
\(656\) −5.26493 + 1.91628i −0.205561 + 0.0748181i
\(657\) −12.0903 + 6.98034i −0.471687 + 0.272329i
\(658\) 0.0866132 + 0.0500061i 0.00337653 + 0.00194944i
\(659\) −3.30453 + 18.7409i −0.128726 + 0.730042i 0.850299 + 0.526301i \(0.176421\pi\)
−0.979025 + 0.203741i \(0.934690\pi\)
\(660\) 0 0
\(661\) 17.6520 + 14.8118i 0.686583 + 0.576111i 0.917922 0.396762i \(-0.129866\pi\)
−0.231339 + 0.972873i \(0.574311\pi\)
\(662\) 17.4916 3.08425i 0.679831 0.119873i
\(663\) 13.9576 38.3481i 0.542067 1.48932i
\(664\) −2.62835 −0.102000
\(665\) 0 0
\(666\) 2.85685 0.110701
\(667\) 11.5740 31.7994i 0.448148 1.23128i
\(668\) 23.8958 4.21348i 0.924558 0.163025i
\(669\) −10.7409 9.01268i −0.415267 0.348450i
\(670\) 0 0
\(671\) −4.33073 + 24.5608i −0.167186 + 0.948158i
\(672\) 0.0651553 + 0.0376174i 0.00251342 + 0.00145112i
\(673\) −9.85260 + 5.68840i −0.379790 + 0.219272i −0.677727 0.735314i \(-0.737035\pi\)
0.297937 + 0.954586i \(0.403701\pi\)
\(674\) −2.24184 + 0.815962i −0.0863523 + 0.0314297i
\(675\) 0 0
\(676\) 5.23548 + 9.06812i 0.201365 + 0.348774i
\(677\) −36.1782 20.8875i −1.39044 0.802771i −0.397076 0.917786i \(-0.629975\pi\)
−0.993364 + 0.115015i \(0.963308\pi\)
\(678\) 18.0309 + 3.17933i 0.692471 + 0.122101i
\(679\) 0.199897 0.167733i 0.00767134 0.00643701i
\(680\) 0 0
\(681\) −5.27501 29.9160i −0.202139 1.14639i
\(682\) −3.29603 + 9.05578i −0.126212 + 0.346764i
\(683\) 9.65205i 0.369325i −0.982802 0.184663i \(-0.940881\pi\)
0.982802 0.184663i \(-0.0591193\pi\)
\(684\) 17.9580 26.4876i 0.686643 1.01278i
\(685\) 0 0
\(686\) 0.307767 + 0.112018i 0.0117506 + 0.00427687i
\(687\) 72.4208 12.7697i 2.76303 0.487196i
\(688\) 6.23734 7.43337i 0.237796 0.283395i
\(689\) −4.60757 + 3.86621i −0.175535 + 0.147291i
\(690\) 0 0
\(691\) 3.58223 6.20461i 0.136275 0.236034i −0.789809 0.613353i \(-0.789820\pi\)
0.926084 + 0.377318i \(0.123154\pi\)
\(692\) −16.7692 + 9.68169i −0.637469 + 0.368043i
\(693\) −0.126936 0.348755i −0.00482191 0.0132481i
\(694\) −14.4726 + 5.26759i −0.549372 + 0.199955i
\(695\) 0 0
\(696\) −12.1438 + 21.0337i −0.460309 + 0.797279i
\(697\) −44.0296 7.76361i −1.66774 0.294068i
\(698\) 6.32836 + 7.54185i 0.239532 + 0.285463i
\(699\) −26.0552 21.8629i −0.985498 0.826931i
\(700\) 0 0
\(701\) −5.58820 2.03394i −0.211063 0.0768208i 0.234325 0.972158i \(-0.424712\pi\)
−0.445388 + 0.895338i \(0.646934\pi\)
\(702\) 22.2035i 0.838019i
\(703\) 1.64482 + 0.414263i 0.0620356 + 0.0156242i
\(704\) −2.16082 −0.0814389
\(705\) 0 0
\(706\) 1.47838 + 8.38429i 0.0556394 + 0.315547i
\(707\) −0.280421 + 0.334193i −0.0105463 + 0.0125686i
\(708\) −7.51056 8.95073i −0.282264 0.336389i
\(709\) −6.60131 + 37.4379i −0.247918 + 1.40601i 0.565701 + 0.824611i \(0.308606\pi\)
−0.813618 + 0.581400i \(0.802505\pi\)
\(710\) 0 0
\(711\) 34.9148 + 60.4742i 1.30941 + 2.26796i
\(712\) 3.03548 + 8.33992i 0.113759 + 0.312552i
\(713\) 6.83465 + 18.7780i 0.255959 + 0.703243i
\(714\) 0.300176 + 0.519920i 0.0112338 + 0.0194575i
\(715\) 0 0
\(716\) 1.49206 8.46188i 0.0557608 0.316235i
\(717\) −35.8698 42.7480i −1.33958 1.59645i
\(718\) −20.2597 + 24.1446i −0.756087 + 0.901069i
\(719\) −1.48425 8.41760i −0.0553532 0.313923i 0.944542 0.328390i \(-0.106506\pi\)
−0.999895 + 0.0144667i \(0.995395\pi\)
\(720\) 0 0
\(721\) −0.0827228 −0.00308076
\(722\) 14.1801 12.6461i 0.527730 0.470639i
\(723\) 1.54330i 0.0573958i
\(724\) −3.94197 1.43476i −0.146502 0.0533225i
\(725\) 0 0
\(726\) −15.5959 13.0865i −0.578819 0.485687i
\(727\) 5.38809 + 6.42127i 0.199833 + 0.238152i 0.856650 0.515899i \(-0.172542\pi\)
−0.656817 + 0.754050i \(0.728097\pi\)
\(728\) 0.0366399 + 0.00646060i 0.00135796 + 0.000239446i
\(729\) 16.6186 28.7842i 0.615503 1.06608i
\(730\) 0 0
\(731\) 72.7620 26.4832i 2.69120 0.979516i
\(732\) −12.6946 34.8781i −0.469205 1.28913i
\(733\) 10.3264 5.96195i 0.381414 0.220210i −0.297019 0.954872i \(-0.595993\pi\)
0.678433 + 0.734662i \(0.262659\pi\)
\(734\) −3.48743 + 6.04040i −0.128723 + 0.222955i
\(735\) 0 0
\(736\) −3.43239 + 2.88011i −0.126519 + 0.106162i
\(737\) −5.35701 + 6.38424i −0.197328 + 0.235166i
\(738\) −40.5088 + 7.14280i −1.49115 + 0.262930i
\(739\) 23.9241 + 8.70767i 0.880063 + 0.320317i 0.742235 0.670140i \(-0.233766\pi\)
0.137828 + 0.990456i \(0.455988\pi\)
\(740\) 0 0
\(741\) 5.44441 21.6169i 0.200005 0.794117i
\(742\) 0.0884842i 0.00324836i
\(743\) −5.45769 + 14.9949i −0.200223 + 0.550109i −0.998648 0.0519860i \(-0.983445\pi\)
0.798425 + 0.602095i \(0.205667\pi\)
\(744\) −2.49050 14.1243i −0.0913061 0.517823i
\(745\) 0 0
\(746\) −9.23447 + 7.74864i −0.338098 + 0.283698i
\(747\) −19.0032 3.35077i −0.695289 0.122598i
\(748\) −14.9326 8.62134i −0.545990 0.315227i
\(749\) −0.0654201 0.113311i −0.00239040 0.00414029i
\(750\) 0 0
\(751\) 1.48505 0.540514i 0.0541903 0.0197237i −0.314783 0.949164i \(-0.601932\pi\)
0.368973 + 0.929440i \(0.379709\pi\)
\(752\) 3.70219 2.13746i 0.135005 0.0779452i
\(753\) −16.6113 9.59055i −0.605350 0.349499i
\(754\) −2.08563 + 11.8282i −0.0759543 + 0.430758i
\(755\) 0 0
\(756\) 0.250221 + 0.209960i 0.00910045 + 0.00763618i
\(757\) 18.9354 3.33882i 0.688217 0.121351i 0.181406 0.983408i \(-0.441935\pi\)
0.506811 + 0.862057i \(0.330824\pi\)
\(758\) −2.33355 + 6.41138i −0.0847584 + 0.232872i
\(759\) 31.1354 1.13014
\(760\) 0 0
\(761\) 12.6228 0.457576 0.228788 0.973476i \(-0.426524\pi\)
0.228788 + 0.973476i \(0.426524\pi\)
\(762\) 9.54161 26.2154i 0.345656 0.949683i
\(763\) −0.217131 + 0.0382860i −0.00786067 + 0.00138605i
\(764\) −14.4491 12.1243i −0.522751 0.438640i
\(765\) 0 0
\(766\) −1.88011 + 10.6626i −0.0679310 + 0.385256i
\(767\) −5.00402 2.88907i −0.180685 0.104318i
\(768\) 2.78500 1.60792i 0.100495 0.0580208i
\(769\) −37.7534 + 13.7411i −1.36142 + 0.495518i −0.916494 0.400048i \(-0.868993\pi\)
−0.444929 + 0.895566i \(0.646771\pi\)
\(770\) 0 0
\(771\) −21.7518 37.6753i −0.783373 1.35684i
\(772\) 15.4105 + 8.89727i 0.554637 + 0.320220i
\(773\) −25.4287 4.48376i −0.914606 0.161270i −0.303512 0.952828i \(-0.598159\pi\)
−0.611094 + 0.791558i \(0.709270\pi\)
\(774\) 54.5729 45.7921i 1.96158 1.64596i
\(775\) 0 0
\(776\) −1.93685 10.9844i −0.0695290 0.394319i
\(777\) −0.0100131 + 0.0275107i −0.000359217 + 0.000986941i
\(778\) 7.52625i 0.269829i
\(779\) −24.3585 1.76162i −0.872735 0.0631164i
\(780\) 0 0
\(781\) 26.1303 + 9.51065i 0.935016 + 0.340318i
\(782\) −35.2112 +